Basic statements which do not seem to contradict themselves, to the best of human knowledge, are called axioms.
It is with respect to these basic statements that we try to investigate the truthfulness of various other composite statements. Such composite statements are called theorems.
A collection of sentences which can be expressed in terms of a number of basic statements by means of $$ \sim , \Rightarrow , \wedge , \vee ,$$ or any other well specified composition is liable to mathematical treatment. By applying various well defined mathematical operations we shall draw conclusions based on the basic statements involved.
The conclusions of various mathematical results or theorems established once shall be used frequently under the conditions stated therein.